# Properties

 Label 345.2 Level 345 Weight 2 Dimension 2771 Nonzero newspaces 12 Newform subspaces 35 Sturm bound 16896 Trace bound 1

# Learn more

## Defining parameters

 Level: $$N$$ = $$345 = 3 \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$35$$ Sturm bound: $$16896$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(345))$$.

Total New Old
Modular forms 4576 3019 1557
Cusp forms 3873 2771 1102
Eisenstein series 703 248 455

## Trace form

 $$2771 q + 5 q^{2} - 19 q^{3} - 35 q^{4} - q^{5} - 65 q^{6} - 36 q^{7} + 9 q^{8} - 23 q^{9} + O(q^{10})$$ $$2771 q + 5 q^{2} - 19 q^{3} - 35 q^{4} - q^{5} - 65 q^{6} - 36 q^{7} + 9 q^{8} - 23 q^{9} - 61 q^{10} + 20 q^{11} - 17 q^{12} - 26 q^{13} + 24 q^{14} - 41 q^{15} - 187 q^{16} - 30 q^{17} - 105 q^{18} - 76 q^{19} - 79 q^{20} - 124 q^{21} - 148 q^{22} - 65 q^{23} - 155 q^{24} - 111 q^{25} - 50 q^{26} - 85 q^{27} - 164 q^{28} - 10 q^{29} - 76 q^{30} - 144 q^{31} - 15 q^{32} - 40 q^{33} - 74 q^{34} - 36 q^{35} - 101 q^{36} - 162 q^{37} - 152 q^{38} - 100 q^{39} - 233 q^{40} - 66 q^{41} - 218 q^{42} - 184 q^{43} - 232 q^{44} - 45 q^{45} - 415 q^{46} - 144 q^{47} - 213 q^{48} - 237 q^{49} - 39 q^{50} - 132 q^{51} - 390 q^{52} - 14 q^{53} - 21 q^{54} - 134 q^{55} - 100 q^{56} - 16 q^{57} - 178 q^{58} - 20 q^{59} + 60 q^{60} - 66 q^{61} + 96 q^{62} + 96 q^{63} + 69 q^{64} + 18 q^{65} + 88 q^{66} + 130 q^{68} + 111 q^{69} - 108 q^{70} + 88 q^{71} + 251 q^{72} + 10 q^{73} + 50 q^{74} + 3 q^{75} - 204 q^{76} - 80 q^{77} - 64 q^{78} - 140 q^{79} - 165 q^{80} - 243 q^{81} - 162 q^{82} - 116 q^{83} - 142 q^{84} - 272 q^{85} - 300 q^{86} - 260 q^{87} - 16 q^{88} - 162 q^{89} - 215 q^{90} - 416 q^{91} - 235 q^{92} - 276 q^{93} - 368 q^{94} - 98 q^{95} - 255 q^{96} - 82 q^{97} - 19 q^{98} - 222 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
345.2.a $$\chi_{345}(1, \cdot)$$ 345.2.a.a 1 1
345.2.a.b 1
345.2.a.c 1
345.2.a.d 1
345.2.a.e 1
345.2.a.f 1
345.2.a.g 2
345.2.a.h 2
345.2.a.i 2
345.2.a.j 3
345.2.b $$\chi_{345}(139, \cdot)$$ 345.2.b.a 2 1
345.2.b.b 2
345.2.b.c 6
345.2.b.d 14
345.2.c $$\chi_{345}(206, \cdot)$$ 345.2.c.a 16 1
345.2.c.b 16
345.2.h $$\chi_{345}(344, \cdot)$$ 345.2.h.a 4 1
345.2.h.b 8
345.2.h.c 8
345.2.h.d 24
345.2.i $$\chi_{345}(47, \cdot)$$ 345.2.i.a 4 2
345.2.i.b 4
345.2.i.c 80
345.2.j $$\chi_{345}(22, \cdot)$$ 345.2.j.a 48 2
345.2.m $$\chi_{345}(16, \cdot)$$ 345.2.m.a 30 10
345.2.m.b 30
345.2.m.c 50
345.2.m.d 50
345.2.n $$\chi_{345}(14, \cdot)$$ 345.2.n.a 40 10
345.2.n.b 400
345.2.s $$\chi_{345}(11, \cdot)$$ 345.2.s.a 160 10
345.2.s.b 160
345.2.t $$\chi_{345}(4, \cdot)$$ 345.2.t.a 240 10
345.2.w $$\chi_{345}(7, \cdot)$$ 345.2.w.a 480 20
345.2.x $$\chi_{345}(2, \cdot)$$ 345.2.x.a 880 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(345))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(345)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 1}$$